41. A sum of money amounts to ₹ 4,840 in 2 years and to ₹ 5,324 in 3 years at compound interest compounded annually. The rate of interest per annum is :

1. 1. 10%

   
   
   

   2. 9%

   
   
   

   3. 11%

   
   
   

   4. 8%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the rate of interest be r% per annum,
   According to the question,
   

   4840 = P		1 +	r		2	..... (i)
   			100

   
   

   and 5324 = P		1 +	r		3	..... (ii)
   			100

   
   On dividing equation (ii) by equation (i), we have,
   

   1 +	r	=	5324	= 1 +	484
   	100		4840		4840

   
   

   ⇒	r	=	484
   	100		4840

   
   ⇒  r = 10%
   Second Method to solve this question :
   Here, b – a = 3 – 2 = 1 and B = Rs 5,324, A = 4,840
   

   R% =		B	− 1		× 100%
   		A

   
   

   Correct Option: A

   Let the rate of interest be r% per annum,
   According to the question,
   

   4840 = P		1 +	r		2	..... (i)
   			100

   
   

   and 5324 = P		1 +	r		3	..... (ii)
   			100

   
   On dividing equation (ii) by equation (i), we have,
   

   1 +	r	=	5324	= 1 +	484
   	100		4840		4840

   
   

   ⇒	r	=	484
   	100		4840

   
   ⇒  r = 10%
   Second Method to solve this question :
   Here, b – a = 3 – 2 = 1 and B = Rs 5,324, A = 4,840
   

   R% =		B	− 1		× 100%
   		A

   
   

   R% =		5324	− 1		× 100%
   		4840

   
   

   R% =		5324 − 4840		× 100%
   		4840

   
   

   R% =	484	× 100% = 10%
   	4840

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42. A man borrowed some money from a private organisation at 5% simple interest per annum. He lended this money to another person at 10% compound interest per annum, and made a profit of Rs. 26,410 in 4 years. The man borrowed

1. 1. Rs. 200000

   
   
   

   2. Rs. 150000

   
   
   

   3. Rs. 132050

   
   
   

   4. Rs. 100000

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the principal be Rs. P.
   

   For 4 years, S.I. =	Principal × Time × Rate
   	100

   
   

   S.I. =	P × 4 × 5	= Rs.	P
   	100		5

   
   

   C.I. = P			1 +	R		T	− 1
   				100

   
   

   C.I. = P			1 +	10		4	− 1
   				100

   
   

   C.I. = P			11		4	− 1
   			10

   
   

   C.I. = P		14641	− 1
   		10000

   
   

   C.I. =	4641P
   	10000

   
   

   Correct Option: D

   Let the principal be Rs. P.
   

   For 4 years, S.I. =	Principal × Time × Rate
   	100

   
   

   S.I. =	P × 4 × 5	= Rs.	P
   	100		5

   
   

   C.I. = P			1 +	R		T	− 1
   				100

   
   

   C.I. = P			1 +	10		4	− 1
   				100

   
   

   C.I. = P			11		4	− 1
   			10

   
   

   C.I. = P		14641	− 1
   		10000

   
   

   C.I. =	4641P
   	10000

   
   According to the question,
   ∴ C.I. - S.I. = 26410
   

   4641P	−	P	= 26410
   10000		5

   
   

   ⇒	4641P − 2000P	= 2641
   	10000

   
   

   ⇒	2641P	= 2641
   	10000

   
   ⇒ P = Rs. 10000

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43. If the difference between the compound and simple interests on a certain sum of money for 3 years at 5% per annum is ₹ 15.25, then the sum is

1. 1. ₹ 2,000

   
   
   

   2. ₹ 1,000

   
   
   

   3. ₹ 1,500

   
   
   

   4. ₹ 2,500

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given in question , Difference = C.I. - S.I. = ₹ 15.25 , Time = 3 years , Rate = 5%
   

   Difference between C.I. and S.I for 3 years =	PR2		300 + R
   	(100)2		100

   
   

   ⇒  15.25 =	P × 25		5 + 300
   	10000		100

   
   

   Correct Option: A

   Given in question , Difference = C.I. - S.I. = ₹ 15.25 , Time = 3 years , Rate = 5%
   

   Difference between C.I. and S.I for 3 years =	PR2		300 + R
   	(100)2		100

   
   

   ⇒  15.25 =	P × 25		5 + 300
   	10000		100

   
   

   ⇒  15.25 =	P × 305
   	400 × 100

   
   

   ⇒  P =	15.25 × 400 × 100	= ₹ 2000
   	305

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44. The difference between the simple and compound interest on a certain sum of money for 2 years at 4% per annum is ₹ 4. The sum is

1. 1. ₹ 2500

   
   
   

   2. ₹ 2,400

   
   
   

   3. ₹ 2,600

   
   
   

   4. ₹ 2,000

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here , Difference = C.I. - S.I. = ₹ 4 , Time = 2 years , Rate = 4%
   Using the given formula ,
   

   Sum = Difference		100		2
   		r

   
   

   Correct Option: A

   Here , Difference = C.I. - S.I. = ₹ 4 , Time = 2 years , Rate = 4%
   Using the given formula ,
   

   Sum = Difference		100		2
   		r

   
   

   Required Sum= 4 ×		100		2	= ₹ 2500
   		4

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45. The difference between simple and compound interest on a certain sum of money for 2 years at 4 percent per annum is ₹ 1. The sum of money is :

1. 1. ₹ 600

   
   
   

   2. ₹ 625

   
   
   

   3. ₹ 560

   
   
   

   4. ₹ 650

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given in question , Difference = C.I. - S.I. = ₹ 1 , , Time = 2 years , Rate = 4%
   

   Sum = Difference ×		100		2
   		r

   
   

   Correct Option: B

   Given in question , Difference = C.I. - S.I. = ₹ 1 , , Time = 2 years , Rate = 4%
   

   Sum = Difference ×		100		2
   		r

   
   

   Sum = 1 ×		100		2	= ₹ 625
   		r

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